Maximum and antimaximum principles for the p-Laplacian with weighted Steklov boundary conditions

Date

2020-03-02

Authors

Cuesta, Mabel
Leadi, Liamidi
Nshimirimana, Pascaline

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We study the maximum and antimaximum principles for the p-Laplacian operator under Steklov boundary conditions with an indefinite weight -Δpu + |u|p-2 u = 0 in Ω, |∇u|p-2 ∂u/∂v = λm(x)|u|p-2 u + h(x) on ∂Ω, where Ω is a smooth bounded domain of ℝN, N > 1. After reviewing some elementary properties of the principal eigenvalues of the p-Laplacian under Steklov boundary conditions with an indefinite weight, we investigate the maximum and antimaximum principles for this problem. Also we give a characterization for the interval of the validity of the uniform antimaximum principle.

Description

Keywords

p-Laplacian, Steklov boundary conditions, Indefinite weight, Maximum and antimaximum principles

Citation

Cuesta, M., Leadi, L., & Nshimirimana, P. (2020). Maximum and antimaximum principles for the p-Laplacian with weighted Steklov boundary conditions. <i>Electronic Journal of Differential Equations, 2020</i>(21), pp. 1-17.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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